lagv2(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 NAME 💅

lagv2 — the 2x2 generalized Schur factor, aka the tiny-but-mighty routine that fixes up your 2-by-2 pencil (A,B) 💖

✨ SYNOPSIS ✨

Functions

  • subroutine dlagv2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr) — double-precision bestie: DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. 🫶
  • subroutine slagv2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr) — single-precision sibling, same energy: SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. 🦋

🌈 Detailed Description 🌈

okay so this page is literally just the Function Documentation for the two routines above — they're twins, one's DOUBLE PRECISION, one's REAL, and the vibes are identical. no cap. 🔥

👑 Function Documentation 👑

🎀 subroutine dlagv2 (double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( 2 ) alphar, double precision, dimension( 2 ) alphai, double precision, dimension( 2 ) beta, double precision csl, double precision snl, double precision csr, double precision snr)

DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. slay. 💅

🌸 Purpose:

DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. This routine computes orthogonal (rotation) matrices given by CSL, SNL and CSR, SNR such that

  1. if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0 types), then
[ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
[  0  a22 ]    [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]

[ b11 b12 ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
[  0  b22 ]    [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ],
  1. if the pencil (A,B) has a pair of complex conjugate eigenvalues, then
[ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
[ a21 a22 ]    [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]

[ b11  0  ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
[  0  b22 ]    [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ]

where b11 >= b22 > 0.

🧚 Parameters

  • A

A is DOUBLE PRECISION array, dimension (LDA, 2). On entry, the 2 x 2 matrix A. On exit, A is overwritten by the "A-part" of the generalized Schur form. 💖

  • LDA

LDA is INTEGER. The leading dimension of the array A. LDA >= 2. (yes it's written THe in the source, we don't gatekeep typos 😭)

  • B

B is DOUBLE PRECISION array, dimension (LDB, 2). On entry, the upper triangular 2 x 2 matrix B. On exit, B is overwritten by the "B-part" of the generalized Schur form. ✨

  • LDB

LDB is INTEGER. The leading dimension of the array B. LDB >= 2.

  • ALPHAR

ALPHAR is DOUBLE PRECISION array, dimension (2).

  • ALPHAI

ALPHAI is DOUBLE PRECISION array, dimension (2).

  • BETA

BETA is DOUBLE PRECISION array, dimension (2). (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may be zero. (!! so watch out 🫣)

  • CSL

CSL is DOUBLE PRECISION. The cosine of the left rotation matrix.

  • SNL

SNL is DOUBLE PRECISION. The sine of the left rotation matrix.

  • CSR

CSR is DOUBLE PRECISION. The cosine of the right rotation matrix.

  • SNR

SNR is DOUBLE PRECISION. The sine of the right rotation matrix.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🍓 Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

📍 Definition at line 155 of file dlagv2.f.

🎀 subroutine slagv2 (real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( 2 ) alphar, real, dimension( 2 ) alphai, real, dimension( 2 ) beta, real csl, real snl, real csr, real snr)

SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. same routine, single precision, still iconic. ⭐

🌸 Purpose:

SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. This routine computes orthogonal (rotation) matrices given by CSL, SNL and CSR, SNR such that

  1. if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0 types), then
[ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
[  0  a22 ]    [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]

[ b11 b12 ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
[  0  b22 ]    [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ],
  1. if the pencil (A,B) has a pair of complex conjugate eigenvalues, then
[ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ]
[ a21 a22 ]    [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ]

[ b11  0  ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ]
[  0  b22 ]    [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ]

where b11 >= b22 > 0.

🧚 Parameters

  • A

A is REAL array, dimension (LDA, 2). On entry, the 2 x 2 matrix A. On exit, A is overwritten by the "A-part" of the generalized Schur form. 💜

  • LDA

LDA is INTEGER. The leading dimension of the array A. LDA >= 2.

  • B

B is REAL array, dimension (LDB, 2). On entry, the upper triangular 2 x 2 matrix B. On exit, B is overwritten by the "B-part" of the generalized Schur form. 🌟

  • LDB

LDB is INTEGER. The leading dimension of the array B. LDB >= 2.

  • ALPHAR

ALPHAR is REAL array, dimension (2).

  • ALPHAI

ALPHAI is REAL array, dimension (2).

  • BETA

BETA is REAL array, dimension (2). (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may be zero. 🫣

  • CSL

CSL is REAL. The cosine of the left rotation matrix.

  • SNL

SNL is REAL. The sine of the left rotation matrix.

  • CSR

CSR is REAL. The cosine of the right rotation matrix.

  • SNR

SNR is REAL. The sine of the right rotation matrix.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🍓 Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

📍 Definition at line 155 of file slagv2.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. (the robots wrote the original, we just gave it main character energy 💀✨)

and that's the whole page bestie! 🫶 this absolute gem lives in LAPACK, Version 3.12.0 — go forth and factor those 2x2 pencils, mwah 💋

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